Computational Mechanics 5 - Boundary Value Problems
01_Revisiting_derivatives
- How to approximate error in approximate derivatives
- How to approximate derivatives using forward difference methods
- How to approximate derivatives using backward difference methods
- How to approximate derivatives using central difference methods
- How to approximate higher order derivatives with forward, backward, and
- central differences
02_Keep_it_steady
- The difference between a PDE and an ODE
- How to approximate differential equations with boundary conditions
- Solve steady-state heat transfer problem
- Solve static deflection of elastic beam
- Demonstrate convergence of finite difference solutions
03_Good_Vibrations
- How to set up and solve an eigenvalue problem
- How eigenvalues and eigenvectors relate to natural frequencies and mode shapes
- How to turn a PDE into a finite difference ODE
- How to use eigenvalues to calculate natural frequencies of a vibrating string
- How to solve a coupled set of ODEs
- Visualize solutions to finite difference equations with 3D plots and
- animations
- How to listen to vibration solutions